Force feedback electrodes in mems accelerometer

ABSTRACT

A microelectromechanical system (MEMS) accelerometer having separate sense and force-feedback electrodes is disclosed. The use of separate electrodes may in some embodiments increase the dynamic range of such devices. Other possible advantages include, for example, better sensitivity, better noise suppression, and better signal-to-noise ratio. In one embodiment, the accelerometer includes three silicon wafers, fabricated with sensing electrodes forming capacitors in a fully differential capacitive architecture, and with separate force feedback electrodes forming capacitors for force feedback. These electrodes may be isolated on a layer of silicon dioxide. In some embodiments, the accelerometer also includes silicon dioxide layers, piezoelectric structures, getter layers, bonding pads, bonding spacers, and force feedback electrodes, which may apply a restoring force to the proof mass region. MEMS accelerometers with force-feedback electrodes may be used in geophysical surveys, e.g., for seismic sensing or acoustic positioning.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.61/785,851, filed Mar. 14, 2013, and U.S. Provisional Application No.61/786,259, filed Mar. 14, 2013, which are incorporated by referenceherein in their entireties.

BACKGROUND

Microelectromechanical system (MEMS) accelerometers are widely used inmany different application areas such as geophysical surveying,underwater imaging, navigation, medical, automotive, aerospace,military, tremor sensing, consumer electronics, etc. These sensorstypically detect acceleration by measuring the change in position of aproof mass, for example, by a change in the associated capacitance.Traditional capacitive MEMS accelerometers may have poor performance dueto low noise suppression and sensitivity, however.

Measurement noise and range may vary for different applications ofsensors. For example, for a navigation application, a measurement rangeof ±20 g may be desired and 1 μg/√Hz measurement noise for this rangecould be tolerated. As another example, a tremor sensing application maydesire a ±1 g measurement range and a lower noise floor of ˜10-100ng/√Hz. One type of noise affecting this noise floor is Brownian noise.Brownian noise refers to noise produced by Brownian motion. Brownianmotion refers the random movement of particles suspended in a liquid orgas resulting from their bombardment by the fast-moving atoms ormolecules in the liquid or gas.

Accelerometers may have many uses in the field of geophysical surveying,particularly marine seismic. For example, in some marine seismicembodiments, a survey vessel may tow one or more streamers in a body ofwater. Seismic sources may be actuated to cause seismic energy to travelthrough the water and into the seafloor. The seismic energy may reflectoff of the various undersea strata and be detected via sensors on thestreamers, and the locations of geophysical formations (e.g.,hydrocarbons) may be inferred from these reflections.

These streamer sensors that are configured to receive the seismic energymay include accelerometers such as those described in this disclosure.(Various other sensors may also be included in some embodiments, such aspressure sensors, electromagnetic sensors, etc.)

Additionally, accelerometers may be used to detect the relativepositions of the streamers (or portions thereof) via acoustic ranging.Acoustic ranging devices typically may include an ultrasonic transmitterand electronic circuitry configured to cause the transceiver to emitpulses of acoustic energy. The travel time of the acoustic energybetween a transmitter and receivers (e.g., accelerometers) disposed at aselected positions on the streamers is related to the distance betweenthe transmitter and the receivers (as well as the acoustic velocity ofthe water), and so the distances may be inferred.

In other marine seismic embodiments, accelerometers according to thisdisclosure may also be used in permanent reservoir monitoring (PRM)applications, for example at a seafloor. Generally, the term“geophysical survey apparatus” may refer to streamers, PRM equipment,and/or sensors that form portions of streamers or PRM equipment.

Accordingly, improvements in accelerometer technology (e.g., allowingbetter performance and/or lower cost) may provide substantial benefitsin the geophysical surveying field, among other fields.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-C are block diagrams illustrating embodiments of a device;

FIG. 2 is a block diagram illustrating one embodiment of a MEMSaccelerometer;

FIGS. 3A-C illustrate an exemplary process flow for the fabrication of acap substrate;

FIGS. 4A-G illustrate an exemplary process flow for the fabrication of afully differential MEMS accelerometer;

FIGS. 5A-E illustrate an exemplary process flow for the etching ofcavities within a substrate; and

FIGS. 6-7 illustrate methods for the use of an accelerometer in ageophysical survey according to this disclosure.

DETAILED DESCRIPTION

This specification includes references to “one embodiment” or “anembodiment.” The appearances of the phrases “in one embodiment” or “inan embodiment” do not necessarily refer to the same embodiment.Particular features, structures, or characteristics may be combined inany suitable manner consistent with this disclosure.

The following paragraphs provide definitions and/or context for termsfound in this disclosure (including the appended claims):

“Comprising.” This term is open-ended. As used herein, this term doesnot foreclose additional structure or steps. Consider a claim thatrecites: “a system comprising a processor and a memory . . . .” Such aclaim does not foreclose the system from including additional componentssuch as interface circuitry, a graphics processing unit (GPU), etc.

“Configured To” or “Operable To.” Various units, circuits, or othercomponents may be described or claimed as “configured to” perform a taskor tasks. In such contexts, “configured to” is used to connote structureby indicating that the units/circuits/components include structure(e.g., circuitry) that performs those task or tasks during operation. Assuch, the unit/circuit/component can be said to be configured to performthe task even when the specified unit/circuit/component is not currentlyoperational (e.g., is not on). The units/circuits/components used withthe “configured to” language include hardware—for example, circuits,memory storing program instructions executable to implement theoperation(s), etc. Reciting that a unit/circuit/component is “configuredto” perform one or more tasks is expressly intended not to invoke 35U.S.C. §112, sixth paragraph, for that unit/circuit/component.Additionally, “configured to” can include generic structure (e.g.,generic circuitry) that is manipulated by software and/or firmware(e.g., an FPGA or a general-purpose processor executing software) tooperate in manner that is capable of performing the task(s) at issue.

“First,” “Second,” etc. As used herein, these terms are used as labelsfor nouns that they precede unless otherwise noted, and do not imply anytype of ordering (e.g., spatial, temporal, logical, etc.). For example,a “first” computing system and a “second” computing system can be usedto refer to any two computing systems. In other words, “first” and“second” are descriptors.

“Based On” or “Based Upon.” As used herein, these terms are used todescribe one or more factors that affect a determination. These terms donot foreclose additional factors that may affect a determination. Thatis, a determination may be solely based on the factor(s) stated or maybe based on one or more factors in addition to the factor(s) stated.Consider the phrase “determining A based on B.” While B may be a factorthat affects the determination of A, such a phrase does not foreclosethe determination of A from also being based on C. In other instances,however, A may be determined based solely on B.

FIGS. 1A-1C show block diagrams illustrating some exemplary embodimentsof a device according to this disclosure (devices 100, 102, and 104,respectively), which differ in their capacitive architecture. Thesedevices include upper substrate 110, interior substrate 130, and lowersubstrate 150. In various embodiments, substrates 110, 130, and 150contain wafers 110 a, 130 a and 130 f (e.g., regions of the wafer onsubstrate 130), and 150 a respectively. In various embodiments, thesewafers may be silicon wafers. As used herein, “wafer” is used broadly torefer to any substrate used for fabricating microelectromechanicalsystem (MEMS) devices. As will be recognized by one skilled in the artwith the benefit of this disclosure, “depositing” material on asubstrate may occur according to various methods common in the MEMSdevice field. In some embodiments, this deposition method is performedas described below with reference to FIGS. 3 and 4. As depicted,interior substrate 130 is split into three portions, proof mass 130 aand anchor regions 130 f. In the illustrated embodiment, these portionsare separated by cavities 130 g. Proof mass 130 a may also be referredto as a proof mass region. Cavities 130 g may be etched by variousmethods recognized by one skilled in the art with the benefit of thisdisclosure, including one embodiment described below with reference toFIG. 5. As is typically the case in accelerometer embodiments, proofmass 130 a undergoes a change in position when the device experiences anacceleration. By measuring the position of proof mass 130 a, themagnitude and direction of the acceleration may be determined.

In the embodiment shown in FIGS. 1A-C, upper substrate 110 is bonded tointerior substrate 130, and lower substrate 150 is also bonded tointerior substrate 130. Bonding may occur using any suitable methodknown in the art. In various embodiments, bonding between substrates 110and 130 and between 150 and 130 occurs using any suitable bondingmethod. In one embodiment, cavity 120 between upper substrate 110 andinterior substrate 130 and cavity 140 between lower substrate 150 andinterior substrate 130 are vacuum-sealed. Cavities 130 g may also bevacuum-sealed. In some embodiments, cavities 120 and 140 may bevacuum-sealed in part by bonding substrates 110, 130, and 150 togetherin a vacuum environment. Substrate 130 may have portions etched awaysuch that vacuum-sealed cavities 130 g, cavity 120, and cavity 140 maybe in fluid communication with each other (e.g., they may possess acommon vacuum).

Turning now to FIG. 1A, a six-capacitor embodiment is shown as device100. Substrates 110, 130, and 150 are divided into two parts: the wafersof each substrate (110 a; 130 a and 130 f together; and 150 a,respectively), and sets of electrodes (these are shown as elements 110b, 110 p, and 110 c; 130 b, 130 p, and 130 c; 130 d, 130 q, and 130 e;150 b, 150 q, and 150 c). These electrodes are typically deposited on aninsulator layer (not shown) such as silicon dioxide, silicon nitride,etc. in order to electrically isolate them from one another, and theyare configured to form the plates of respective capacitors. Two sets ofelectrodes are deposited/situated/disposed on interior substrate 130:the first set being on the upper surface, forming electrodes 130 b, 130p, and 130 c; and the second set being on the lower surface, formingelectrodes 130 d, 130 q, and 130 e. Said differently, the sets ofelectrodes on the interior substrate are deposited on the top and bottomof the interior substrate, or on opposite sides of the interiorsubstrate. (Note that the phrase “opposite sides” of a structure such asa substrate is not limited to the top and bottom of a structure;instead, the phrase may be used to variously refer to the left and rightsides of a structure, or the front and back sides of a structure. Ofcourse, the characterization of different portions of a structure astop, bottom, left, right, front, and back depends on a particularvantage point.)

In one embodiment, a set of electrodes is deposited on the lower surfaceof upper substrate 110, forming electrodes 110 b, 110 p, and 110 c. Aset of electrodes is also deposited on the upper surface of lowersubstrate 150, forming electrodes 150 b, 150 q, and 150 c. Both of thesesets of electrodes on upper substrate 110 and lower substrate 150 may bereferred to as a set of electrodes deposited, situated, or disposed on asurface opposing a surface of interior substrate 130 (i.e., therespective upper and lower surfaces of interior substrate 130). In someembodiments, the sets of electrodes may be deposited as metallic layerson each substrate.

In the embodiment shown in FIG. 1A, the set of electrodes on the uppersubstrate 110 and the opposing set of electrodes on the upper surface ofinterior substrate 130 are configured to form three capacitors. (E.g.,electrodes 110 b and 130 b are configured to form one capacitor;electrodes 110 p and 130 p a second capacitor; and electrodes 110 c and130 c, the third capacitor.) Similarly, the set of electrodes on lowersubstrate 150 and the opposing set of electrodes on the lower surface ofinterior substrate 130 are configured to form three capacitors.

As used herein, “opposing” surfaces are those that face each other.“Opposing” surfaces may be on the same substrate or on differentsubstrates. For example, electrodes 130 b and 130 d are on opposingsurfaces of substrate 130; electrodes 110 b and 130 b are on opposingsurfaces of different substrates. As shown, in this embodiment theelectrodes on opposing surfaces of different substrates may be formedsuch that they are in corresponding positions. This arrangement allowseach pair of electrodes (e.g., 110 b and 130 b) to act as plates of acapacitor. As used herein, the term “deposited” refers to anyfabrication technique in which a type of material is placed on at leasta portion of an underlying material or layer.

The term “layer” is to be construed according to its ordinary usage inthe art, and may refer to a material that covers an entire portion ofone or more underlying materials, as well as discrete regions situatedon top of the underlying material(s). Accordingly, a “layer” may be usedto refer, for example, to the set of electrodes 130 b, 130 p, and 130 cdepicted in FIG. 1A, which may result from a continuous deposition ofmaterial that is deposited and then partially etched away. In someembodiments—for example as described below with reference to FIG. 4—acertain layer may fall “below” another layer that was deposited firstbecause the first deposited layer is not continuous. For example, adeposition of a piezoelectric material may be processed such that thelayer contains discrete portions. Accordingly, when another spring layeris deposited, some portions of the spring layer may fall “below” thepiezoelectric layer since it is not continuous. Thus, portions of thespring layer may appear to be at the same vertical level as thepiezoelectric layer. Accordingly, in some instances, the term “layer”refers to the order of deposition, and not necessarily the verticalposition (e.g., height) of materials in reference to one another.

Continuing with the discussion of FIG. 1A, the capacitors formed byelectrodes 110 b and 130 b, 110 c and 130 c, 130 d and 150 b, and 130 eand 150 c may all be used as sense capacitors. What is meant by this isthat they are operable to detect the movement of proof mass 130 a byusing a system configured to detect changes in the capacitances. Becausesets of electrodes deposited on the substrates are used for sensing theacceleration in device 100, these electrodes may be referred to assensing electrodes or sense electrodes. The system detecting the changesin the capacitances may be any system that is configured to use thecapacitances—for example, a closed-loop readout circuit. In otherembodiments, along with vacuum packaging and piezoelectric damping, thiscapacitive architecture may be used in closed-loop accelerometersystems, as well as any other resonating MEMS structure. Together, thefour capacitors may form a fully differential architecture. In oneinstance, as proof mass 130 a is displaced along the Z-axis 155 by anapplied acceleration, two of the capacitors are increasing incapacitance, while the other two are decreasing equally. The differencesin capacitances in each capacitor, as measured by any system configuredto use capacitances, indicate the position of proof mass 130 a. Incertain embodiments, with proper full bridge connection of these fourcapacitors, the architecture of device 100 may avoid some of thedisadvantages in traditional capacitive sensing architectures—forexample, less sensitivity, low noise suppression, and low SNR. Thesedisadvantages may arise in part from Brownian noise.

In other embodiments, however, a simpler capacitive architecture may beused. For example, two sense capacitors may be used instead of four. Inthis embodiment, the capacitors may be arranged such as proof mass 130 ais displaced along the Z-axis by an applied acceleration, one capacitoris increasing in capacitance, while the other is decreasing. This isknown as a “differential” architecture, in that the difference betweencapacitances is the figure of merit.

In yet other embodiments, a single sense capacitor may be used. In thatembodiment, as proof mass 130 a is displaced along the Z-axis in onedirection by an applied acceleration, the capacitance increases; asproof mass 130 a is displaced along the Z-axis in the other direction,the capacitance decreases. This embodiment may be referred to as a“single-ended” capacitive architecture.

A differential architecture typically provides a higher S/N ratio than asingle-ended architecture, and a fully differential architecturetypically provides even further S/N improvement. The differential andsingle-ended designs may be used in accordance with the presentdisclosure, however.

Continuing with the discussion of FIG. 1A, the capacitors formed byelectrodes 110 p and 130 p, and 130 q and 150 q, respectively may beused as force feedback capacitors. In some embodiments of known devices,a capacitor may be used as both a sense capacitor and a force feedbackcapacitor, e.g. with the use of switching electronics. In suchembodiments, only a portion (typically 50%) of the capacitor's dutycycle is allocated to each task, which may limit the maximum feedbackforce that can be applied.

According to the present disclosure, however, the use of separate forcefeedback electrodes may provide for continuous feedback, which maysubstantially increase the dynamic range compared to designs that switchthe function of a capacitor according to a duty cycle. Further, thedesign of a device according to this disclosure may further besimplified through the omission of switching circuitry.

In the embodiment shown in FIG. 1A, device 100 is configured to performin a fully differential capacitive architecture. As shown, the fourouter capacitors (i.e., those formed by electrodes 110 b and 130 b, 110c and 130 c, 130 d and 150 b, and 130 e and 150 c, respectively) act assense capacitors, and the two inner capacitors (i.e., those formed byelectrodes 110 p and 130 p, and 130 q and 150 q, respectively) act asforce feedback capacitors. In other embodiments, the various capacitorsmay take on other roles. For example, the outer capacitors may form fourforce feedback capacitors, and the inner capacitors may form sensecapacitors. It may be advantageous in some embodiments for the forcefeedback capacitor(s) to be symmetric with respect to the center of massof proof mass 130 a. This feature may allow the force feedbackcapacitors to provide a linear restoring force without providing atorque.

The fully differential capacitive architecture embodiment depicted inFIG. 1A may allow the differences between capacitors (e.g., voltage,current, or capacitance) to be measured by another circuit (not shown).In some embodiments, a fully differential capacitive architecture mayallow the capacitors to be connected using a full bridge connection or aWheatstone bridge connection. In another embodiment, the fullydifferential capacitive architecture may be connected to differentialreadout circuitry, for example, using a differential operationalamplifier. In some embodiments, these configurations may avoid thedisadvantages of a low signal-to-noise ratio found in traditional MEMSaccelerometers.

In addition, the architecture shown in FIG. 1A allows measurement ofacceleration along an axis that perpendicularly intersects substrates110, 130, and 150 (referred to as the “Z-axis” herein). Because proofmass 130 a is separated from anchor regions 130 f by cavities 130 g,anchor regions 130 f act as an anchor/stabilizer when proof mass 130 amoves upwards and downwards along Z-axis 155. This movement leads toslight variations in the position of proof mass 130 a, which leads toslight changes in the capacitance of the capacitors arranged in thefully differential architecture. This change in capacitance allows thecapacitors to detect a change in the position of proof mass 130 a. Thefully differential capacitive architecture shown in FIG. 1 thus allows aZ-axis acceleration to be measured. In another embodiment, device 100may contain additional electrodes or capacitors situated surroundinginterior substrate 130. With additional structural modifications, knownto one skilled in the art, these additional electrodes or capacitorsallow measurement of the acceleration of proof mass 130 a as it movesside-to-side (i.e., to the left or right of interior substrate 130) orfront-to-back (i.e., into and out of sheet 1). In such an embodiment,device also includes lateral accelerometer capabilities. Accordingly, inone embodiment, device 100 may measure acceleration along Z-axis 155, aswell as in an X-Y plane perpendicular to Z-axis 155 (i.e., a planeparallel to substrate 130). This allows an acceleration to be measuredor detected in three dimensions.

Force feedback electrodes as shown in FIG. 1A may be used to maintainproof mass 130 a relatively close to its equilibrium, or rest, position.By design, proof mass 130 a tends to deviate from its equilibriumposition as device 100 undergoes acceleration; however by maintainingproof mass 130 a relatively close to the equilibrium position, thesystem may be maintained in an approximately linear region of operation.Compared to an embodiment that does not use force feedback, this mayallow for an increased range of accelerations measurable by device 100.In some embodiments, the output of device 100 may be based on the amountof force necessary to maintain proof mass 130 a at or near itsequilibrium position, because this amount is directly related to theacceleration being experienced by device 100.

In other embodiments, electrodes may be formed such that only one sensecapacitor and only one force feedback capacitor are used. In yet otherembodiments, various numbers of sense capacitors and various numbers offorce feedback capacitors may be used.

As noted above, Brownian noise is an important consideration in thedesign of devices such as device 100. The Brownian noise associated witha sensor such as a MEMS accelerometer may be represented by thefollowing equation:

Noise_(MEMS)= √4k _(B) Tb /M

In this equation, k_(B) is Boltzmann's constant (1.381×10⁻²³ J/K), Trepresents the ambient temperature in K, b represents the dampingcoefficient in N s/m, and M represents the mass of the resonatingstructure. As can be seen by this equation, the Brownian noise of thesystem can be decreased by increasing the mass and decreasing the airdamping of the system. By designing a huge mass for the accelerometer,thermal noise can be decreased down to on the order of hundreds ofng/√Hz levels, but practically, MEMS devices are not typically designedwith such large sensor dimensions.

A high vacuum level may be used to decrease the Brownian noise byreducing the quantity of random interactions of air molecules with thesensor. Accordingly, the use of a vacuum may in some embodiments reducethe noise floor of the system to ng/√Hz levels. Thus in someembodiments, the use of a vacuum-sealed cavity, for example 120, 130 g,and 140, may reduce the Brownian noise inside device 100.

The use of a vacuum may, however, in some embodiments, increase theresonant quality factor of the system greatly. In some embodiments, thequality factor may increase to levels over 10,000. Such a high qualityfactor may contribute to undesirable instabilities in the operation ofdevice 100. In some embodiments, piezoelectric damping may be used to atleast partially counteract the effect of the high vacuum level.Piezoelectric damping transforms the kinetic oscillation energy of anaccelerometer to electrical energy that may be dissipated outside thesystem, for example, by connecting the piezoelectric structures to atunable external load (e.g., a tunable resistive load). Thus the qualityfactor may be decreased to manageable levels.

Besides the effects of Brownian noise on measurement noise andmeasurement range, non-linearities may affect the performance of MEMSdevices. As one skilled in the art with the benefit of this disclosurewill recognize, non-linearity of a MEMS device may be affected byfrequency response, sensing architecture, springs, and/or the readoutcircuit. In particular, an accelerometer may have a region ofapproximate linearity while the proof mass is near its rest orequilibrium position. However, the farther the proof mass travels fromits rest position, the readout may depart from the ideal linearresponse.

As noted above, the non-linearities in device 100 may in someembodiments be reduced by using a closed-loop readout circuit, which maybe used to stabilize proof mass 130 a within a MEMS accelerometer to theregion of its equilibrium position via the use of force feedbackelectrode(s). For example, a closed loop Σ−Δ circuit may be used.

In certain embodiments, a closed-loop readout circuit includes thesensing capacitors, as well as one or more force feedback electrodes.With these elements connected in a closed loop, the accelerometer mayadjust the position of the proof mass to maintain linear operation,using the acceleration detected by the capacitors and a force applied bythe force feedback electrodes. Thus, using a closed-loop circuitarchitecture with a MEMS accelerometer may avoid some of thedisadvantages of such non-linearities.

Turning now to FIG. 1B, device 102 is shown. Device 102 is broadlysimilar to device 100, discussed above (and with corresponding referencenumerals), but it has a different capacitive architecture. FIG. 1Bdepicts a “differential,” rather than a “fully differential” capacitivearchitecture. What is meant by this is that only two sense capacitorsare used, instead of four.

In the embodiment depicted as device 102, for example, the capacitorsformed by electrodes 110 c and 130 c, and 130 e and 150 c, respectively,may be used as sense capacitors. The capacitors formed by electrodes 110p and 130 p, and 130 q and 150 q, respectively, may be used as forcefeedback capacitors. In other embodiments, these roles may be changed;however, it may in some embodiments be advantageous for the forcefeedback capacitors to be symmetric with respect to the center of massof proof mass 130 a, as discussed above.

Turning now to FIG. 1C, another related device, device 104, is shown.Device 104 is broadly similar to device 102, discussed above (and withcorresponding reference numerals), but the capacitors are arrangeddifferently.

In this embodiment, four capacitors are disposed symmetrically on device104. These may be used, in various embodiments, as either sense or forcefeedback capacitors. For example, the capacitors formed by electrodes110 p and 130 p, and 130 e and 150 c, respectively, may be used as sensecapacitors. The capacitors formed by electrodes 110 c and 130 c, and 130q and 150 q, respectively, may be used as force feedback capacitors. Inother embodiments, these roles may be changed; however, it may in someembodiments be advantageous for the force feedback capacitors to besymmetric with respect to the center of mass of proof mass 130 a, asdiscussed above.

Turning now to FIG. 2, a block diagram illustrating one embodiment of aMEMS accelerometer 200 is shown. As depicted, accelerometer 200 includesupper substrate 210, interior substrate 230, and lower substrate 250. Invarious embodiments, substrates 210, 230, and 250 contain wafers 210 a,230 a and 230 f together, and 250 a respectively, all of which aresimilarly numbered to FIGS. 1A-1C, and may be configured as describedabove with reference to those figures. Additionally, in the embodimentshown, the wafer of interior substrate 230 is split into three portions,proof mass 230 a and anchor regions 230 f. In the illustratedembodiment, these portions are separated by cavities 230 g and boundedby protection structures 230 h. In one embodiment, protection structures230 h may be silicon dioxide. In this embodiment, cavity 220 betweenupper substrate 210 and interior substrate 230, cavity 240 between lowersubstrate 250 and interior substrate 230, and cavities 230 g arevacuum-sealed. By vacuum-sealing, or vacuum-packaging, these cavities,certain embodiments of accelerometer 200 may avoid some of thedisadvantages of Brownian noise discussed above.

Interior substrate 230 may include several parts: the silicon wafer,composed of proof mass 230 a and anchor regions 230 f; cavities 230 g(which may in some embodiments become vacuum-sealed cavities duringprocessing), bounded by protection structures 230 h; sets of electrodes230 b and 230 c; spring layers 230 d and 230 e; piezoelectric structures230 j; and pairs of electrodes 230 k situated on piezoelectricstructures 230 j. In one embodiment, substrates 210 and 250 are dividedinto four parts: the wafers of each substrate, 210 a and 250 arespectively; sets of electrodes 210 b and 250 b respectively; oxidelayers, 210 c and 250 c respectively; and getter layers 210 d and 250 d.In this embodiment, the central ones of electrodes 210 b, 230 b, 230 c,and 250 b may be used as separate force feedback electrodes. The otherones of those electrodes may be used as sensing electrodes.

In the embodiment shown in FIG. 2, upper substrate 210 is bonded tointerior substrate 230, and lower substrate 250 is bonded to interiorsubstrate 230 as well. In various embodiments of FIG. 2, bonding betweensubstrates 210 and 230 and between 250 and 230 occurs using any suitablebonding technique. As depicted, substrates 210, 230, and 250 are bondedto each other using bonding structures 260. Bonding structures 260 maybe composed of any material known to one skilled in the art that maysuitably vacuum seal cavities 220 and 240. In one embodiment, bondingstructures 260 may be composed of silicon dioxide; in another, ametallic material or composition such as copper and tin. In otherembodiments, bonding structures 260 may be composed of metalliccompositions such as gold and tin, or aluminum and germanium.Alternately, bonding structures 260 may be composed of both silicondioxide and metallic contacts. Cavities 220 and 240 may be vacuum-sealedin part by bonding structures 260. Substrates 210, 230, and 250 may alsoassist in vacuum-sealing cavities 220 and 240. In some embodiments,cavities 220 and 240 may be vacuum-sealed in part by bonding substrates210, 230, and 250 together. Spring layers 230 d and 230 e may haveportions etched away such that vacuum-sealed cavities 230 g, 220, and240 may be in fluid communication with each other (e.g., they maypossess a common vacuum). Thus, this vacuum-sealed cavity may be boundedin part by upper substrate 210, lower substrate 250, and protectionstructures 230 f. Bonding structures 260 and substrate 230 may alsobound in part the common vacuum throughout cavities 220, 230 g, and 240.

In one embodiment, spring layers 230 d and 230 e are grown on opposingsurfaces of interior substrate 230. In addition, as used herein, theterm “grown” refers to any fabrication technique in which a type ofmaterial is formed on at least a portion of an underlying material orlayer. This may be accomplished, for example, by heating that materialor layer to high temperatures, by wet oxidation, etc. For example,heating a silicon substrate to high temperatures may create bonds withoxygen atoms in the air so that silicon dioxide is formed. Thus aninsulating silicon dioxide layer may be formed using thermal oxidationof silicon. Spring layers 230 d and 230 e may be composed of an oxidesuch as silicon dioxide. Spring layers 230 d and 230 e allow proof mass230 a to vary in position within interior substrate 230, with anchorregions 230 f assisting by adding stability to interior substrate 230.Vacuum-sealed cavities 230 g may assist in avoiding noise (e.g.,Brownian noise) caused by the impingement of gas particles on proof mass230 a. Oxide layers 210 c and 250 c are grown, or disposed, on the lowersurface of upper substrate 210 and the upper surface of lower substrate250, respectively. Oxide layers 210 c and 250 c may be composed ofsilicon dioxide. Getter layers 210 d and 250 d, which assist inmaintaining the common vacuum of vacuum-sealed cavities 220, 240, and230 g, are deposited on oxide layers 210 c and 250 c. In someembodiments, getter layers 210 d and 250 d may be deposited on anyportion of substrates 210, 230, and 250 exposed to the vacuum-sealedcavity. In one embodiment, a single getter layer may exist withinaccelerometer 200, deposited on some portion of substrates 210, 230,and/or 250. Getter layers 210 d and 250 d may be composed of anysuitable material known to those skilled in the art, and may assist, insome embodiments, in avoiding some of the disadvantages of Browniannoise within vacuum-sealed cavities 220, 230 g, and 240.

As shown, two sets of electrodes 230 b and 230 c may be deposited onspring layers 230 d and 230 e—the first on the upper surface of interiorsubstrate 230; and the second, on the lower surface. Said differently,sets of electrodes 230 b and 230 c may be deposited on opposite sides ofthe interior substrate. A set of electrodes 210 b is deposited on thelower surface of upper substrate 210. A set of electrodes 250 b is alsodeposited on the upper surface of lower substrate 250. Both sets ofelectrodes 210 b and 250 b on upper substrate 210 and lower substrate250 respectively may be referred to as a set of electrodes deposited onan opposing surface from the upper and lower surface respectively ofinterior substrate 230.

In the embodiment shown, sets of electrodes 210 b and 230 b areconfigured to form three capacitors. Similarly, sets of electrodes 230 cand 250 b are configured to form three capacitors. Overall, by formingthese six capacitors, accelerometer 200 is configured to perform in afully differential capacitive architecture with separate force feedbackelectrodes, for example, as described above with reference to FIG. 1A.Accordingly, in the embodiment depicted in FIG. 2, the fullydifferential capacitive architecture may allow the capacitors to operatetogether to detect changes in an acceleration of proof mass 230 a as itmoves upwards and downwards along Z-axis 155. For example, thecapacitors formed by sets of electrodes 210 b, 230 b, 230 c, and 250 cmay detect an acceleration of accelerometer 200. Then, a closed-loopcircuit or system may determine an acceleration of accelerometer usingthe measured electrical current, change in capacitance, or change involtage of these capacitors. In some embodiments, this closed-loopcircuit or system may be referred to as front-end readout circuitry,which may use a differential operational amplifier configuration. Insome embodiments, accelerometer 200 may contain additional electrodes orcapacitors situated surrounding interior substrate 230. With additionalstructural modifications known to one skilled in the art theseadditional electrodes or capacitors allow measurement of acceleration inan X-Y plane perpendicular to Z-axis 155. Such modifications would allowacceleration to be measured or detected in three dimensions.

In one embodiment, accelerometer 200 also includes piezoelectricstructures 230 j disposed on spring layers 230 d and 230 e.Piezoelectric structures 230 j may be composed of any piezoelectricmaterial. Piezoelectric structures 230 j translate mechanical energyfrom spring layers 230 d and 230 e into electrical energy, which may bedissipated externally via pairs of electrodes 230 k disposed on eachpiezoelectric structure 230 j. The piezoelectric material may bend dueto the movement of proof mass 130 a, which is translated to mechanicalenergy by spring layers 230 d and 230 e. The addition of thispiezoelectric damping may reduce the Q-factor of accelerometer 200. TheQ-factor may be adjusted by tuning the load connected to electrodes 230k.

FIGS. 3A-C illustrate an exemplary process flow for the fabrication of acap substrate (e.g., a substrate similar substrate 110 or substrate210). Turning now to FIG. 3A, substrate 310 may be a silicon wafer,etched for the later deposition of getter layers. Layer 320 is depositedor grown on substrate 310. Layer 320 may be further patterned. In oneembodiment, layer 320 may be silicon dioxide.

Turning now to FIG. 3B, a set of electrodes 350 and metallic contacts360 and 365 are deposited on layer 320. Notably, the set of electrodes350 are isolated from one another on layer 320. Set of electrodes 350may be any type of metallic contact. Metallic contacts 360 and 365 mayin some embodiments be made of chromium, copper and tin, gold and tin,aluminum and germanium, etc., which may be patterned with any suitablemethod, such as lift-off or etching. In this embodiment, layer 320 ispatterned further for the deposition of metallic contacts 365. In otherembodiments, metallic contacts 360 and 365 may be deposited on anotherlayer, which may be silicon dioxide, especially patterned for theirdeposition. This additional layer may be deposited partially on layer320, for example, deposited only in the regions of metallic contacts 360and 365.

Turning now to FIG. 3C, spacers 370 are deposited on layer 320. In someembodiments, spacers 370 may also be deposited on another layer, whichmay be silicon dioxide, especially patterned for their deposition. Asdepicted, spacers 370 may be silicon dioxide. In some embodiments,metallic contacts 360 and 365 and spacers 370 may operate as a bondingregion to be bonded to another substrate as described below withreference to FIGS. 4A-G. In one embodiment, spacers 370 may be referredto as bonding spacers.

FIGS. 4A-G illustrate an exemplary process flow for the fabrication of afully differential MEMS accelerometer with a separate force feedbackelectrode, according to one embodiment of this disclosure. Turning nowto FIG. 4A, substrate 430 may be a silicon wafer. Trenches 415 may befilled with silicon dioxide. In one specific embodiment, trenches 415may be 3 μm wide. To fill trenches 415, trenches 415 may be etched firstby any method known to one skilled in the art. For example, in oneembodiment, using deep reactive-ion etching (DRIE), 3 μm wide trenchesare opened on the silicon wafer. Then, to fill trenches 415, oxide isgrown on the surface of substrate 430. In another embodiment, this oxidemay be used as a masking layer for etching in later fabrication stages,for example, XeF₂ (gaseous) etching to remove portions of substrate 430.The depth of trenches 415 may affect the thickness of the accelerometerproof mass because substrate 430 is part of the fully fabricatedaccelerometer. Referring briefly to FIG. 4D, because trenches 415isolate proof mass 430 a from anchor regions 430 f, trenches 415 may bereferred to as isolation trenches. Trenches 415 may also protect proofmass 410 a and anchor regions 410 f from possible later etching steps.Thus trenches 415 may also be referred to as protection trenches. Layer420 is deposited/grown on substrate 430, also covering trenches 415.Layer 420 may be silicon dioxide. In one embodiment, layer 420 may alsobe patterned for deposition of subsequent layers or deposited portions.In this accelerometer embodiment, layer 420 may be referred to as a“spring layer.” One of ordinary skill in the art will understand thatlayer 420 may be of any suitable thickness according to designparameters. In one specific embodiment, the thickness of layer 420 maybe 4 μm.

Turning now to FIG. 4B, metallic contacts 425 are deposited andpatterned for deposition of piezoelectric structures 432. Metalliccontacts 425 may be various metals, known to one skilled in the art.Piezoelectric structures 432 may be various piezoelectric materials,known to one skilled in the art. To form piezoelectric structures 432,piezoelectric material is deposited. In certain embodiments, bothmetallic contact 425 and piezoelectric structure 432 may be referred toas the piezoelectric structure.

Turning now to FIG. 4C, layer 440 is deposited/grown on layer 420 andpatterned to protect the side walls of piezoelectric structures 432.Layer 440 may be silicon dioxide. Then top metallization is deposited onlayer 440. This metallic deposition forms set of electrodes 450. Set ofelectrodes 450 are deposited so that the electrodes are isolated fromeach other on layer 440. In one embodiment with a further etching step,set of electrodes 450 may also be patterned. Layer 440 may also includeanother thin layer of silicon dioxide. That layer may be patterned sothat the bonding regions, the regions extending laterally outwards frompiezoelectric structures 432 (or the region surrounding and includingbonding pads 427) are defined for the later bonding of spacers 460,which are depicted in FIG. 4D. These bonding regions may also bereferred to as wafer bonding areas. Bonding pads 427 are deposited inthe same metallic deposition as sets of electrodes 450. In oneembodiment, bonding pads 427 may also be patterned, for example,especially for later bonding of a cap wafer. Finally, in the samemetallic deposition, pairs of electrodes 455 are deposited onpiezoelectric structures 432 and partially on layer 440. In the waferbonding areas, set of electrodes 450, and pairs of electrodes 455,chromium may be patterned with lift off. In another embodiment, bondingpads 427, sets of electrodes 450, and pairs of electrodes 455 may bedeposited and patterned in separate steps. For example, these elementsmay be deposited or electroplated. In some embodiments, the metals usedfor bonding pads 427, sets of electrodes 450, and pairs of electrodes455 may be gold, aluminum, or chromium.

Turning now to FIG. 4D, cap wafer 475 is bonded to substrate 430 by anybonding process known to one skilled in the art. As part of substrate430, proof mass 430 a is bounded in part by trenches 415, as well asspring layers 420 and 480. Spacers 460 may be aligned with the bondingregion on substrate 430, and bonding pads 427 may be aligned with anopposing contact on cap wafer 475 between bonding spacers 460. In someembodiments, for example in accelerometer 200 as described above withreference to FIG. 2, the bonding process may establish the height ofcavities 220 and 240 such that the capacitors formed by the electrodeshave desired values. Because of this bonding process, in one embodiment,spacers 460 may be referred to as bonding spacers. In some embodiments,cap wafer 475 may be a cap wafer fabricated by the process illustratedin FIG. 3. Thus cap wafer 475 contains layer 470, which may be silicondioxide, isolating the set of electrodes on cap wafer 475 opposing setof electrodes 450.

During this bonding process, set of electrodes 450 are aligned to opposethe set of electrodes on cap wafer 475 so that at least a portion ofthese sets of electrodes may form the capacitors to be used in a fullydifferential capacitive architecture. According to any suitable bondingprocess, the spacing of set of electrodes 450 from the set of electrodeson cap wafer 475 may be determined in order to give the capacitorsformed thereby their desired values. In certain embodiments, the centerelectrode of set of electrodes 450 and the opposing electrode on capwafer 475 may form electrode contacts to be used for force feedback.That is, these electrodes are operable to apply a feedback force toproof mass 430 a.

MEMS accelerometers, in order to operate in a regime of approximatelinearity, may use electrodes to apply a force to the proof mass. In theembodiment depicted in FIG. 4D, the center electrode of set ofelectrodes 475 and the opposing electrode on cap wafer 475 may formelectrode contacts to be used for force feedback. In some embodiments,this may avoid some of the disadvantages of MEMS accelerometers that useelectrodes for sensing and force feedback at the same time. Certain MEMSaccelerometers may switch between integration and feedback in a closedloop circuit, which may increase circuit complexity and may decrease themaximum feedback force applied. For example, because only a portion(typically 75-80%) of the duty cycle of such a switched-functionelectrode is available for force feedback, only a limited amount offeedback force may be applied.

But to operate in a closed loop circuit, accelerometers may need toapply force to the proof mass or structure. Thus in the embodimentshown, separate electrodes (in this embodiment, the center electrode ofset of electrodes 450 and the opposing electrode on cap wafer 475) areused to apply force to the proof mass. Because these electrodes are usedsolely to apply force, these electrodes may be referred to as forcefeedback electrodes. These force feedback electrodes may receivefeedback from an external circuit based on measurements taken at thesense electrodes to apply a force to the proof mass region, which mayallow accelerometer 400 to avoid operating in a non-linear manner. Suchforce feedback electrodes may also allow accelerometer 400 to avoidswitching complexity from an external circuit and may increase themeasurement range of accelerometer 400.

The readout of such an accelerometer with separate force feedbackelectrodes may also be simplified. In one embodiment, the readout maysimply be based on the force applied by the feedback electrodes. This isdue to the fact that, in order to keep the proof mass near itsequilibrium position, a force is required that is proportional to theoverall acceleration being experienced by the accelerometer.

As shown in FIG. 4D, after cap wafer 475 is bonded to substrate 430,substrate 430 is ground from bottom up to the tip of trenches 415. (Insome embodiments, substrate 410 may be ground somewhat beyond the tipsof trenches 415.) Then layer 480 is grown/deposited on the bottom (ormay be referred to as backside) of substrate 430. One of ordinary skillin the art will recognize that layer 480 may be of any suitablethickness according to design requirements. In one specific embodiment,the thickness of layer 480 may be 4 μm. In this accelerometerembodiment, layer 480 is referred to as a spring layer.

Turning now to FIG. 4E, layer 481, piezoelectric structures 486(including metallic contacts), set of electrodes 490, pairs ofelectrodes 493, and bonding pads 494 are deposited onto layer 480 usingthe same or a similar process as outlined above with reference to FIGS.4A-C, with similar corresponding elements.

Turning now to FIG. 4F, substrate 430 may be etched to form cavitiesbetween trenches 415 as described below with reference to FIG. 5. Forexample, XeF₂ gas may be used to etch the cavities. After etching, proofmass 430 a is separated from anchor regions 430 f by isolation trenches415 and the cavities defined thereby, which may become vacuum-sealed ina later processing step.

Turning now to FIG. 4G, cap wafer 495 is bonded to substrate 430 usingthe same or similar process described above with reference to FIG. 4D.Spacers 460 may be aligned with the bonding region on substrate 430, andbonding pads may be aligned with an opposing contact on cap wafer 495between bonding spacers 460 using known techniques. In some embodiments,cap wafer 495 may be a cap wafer fabricated by the same or similarprocess illustrated in FIG. 3. Thus cap wafer 495 contains layer 470,which may be silicon dioxide, isolating the set of electrodes on capwafer 495 opposing the corresponding set of electrodes on substrate 430.At least a portion of these sets of electrodes may form the capacitorsto be used in a fully differential capacitive architecture, and aseparate portion may be used to form force feedback electrodes. Thussubstrate 430 and cap wafers 475 and 495 are now fabricated to form, inthis embodiment, a fully differential MEMS accelerometer. In certainembodiments, the bottom center electrode of substrate 430 and centerelectrode on cap wafer 495 may be selected to form electrode contacts tobe used for force feedback. The use of electrodes at the center of proofmass 430 a for force feedback may have the advantageous effect ofapplying a linear force, but no torque, to proof mass 430 a. In someembodiments, for example in accelerometer 200, this last bonding stepmay form a common vacuum-sealed cavity throughout cavities 220, 230 g,and 240.

FIGS. 5A-E illustrate an exemplary process flow for the etching ofcavities within a substrate. Turning now to FIG. 5A, substrate 530 maybe a silicon wafer. Trenches 515 may be etched by any method known toone skilled in the art. For example, in one embodiment, using deepreactive-ion etching (DRIE), 3 μm wide trenches are opened on thesilicon wafer. Trenches 515 may be used as protection layers, orprotection structures, during the later isotropic release processes. Thedepth of trenches 515 may affect the thickness of the accelerometerproof mass. In an accelerometer implementation, for example inaccelerometer 200, trenches 515 may be referred to as protectiontrenches.

Turning now to FIG. 5B, trenches 515 are grown/filled/deposited, with anoxide, for example silicon dioxide conformally. This filling processdeposits a layer of oxide on the surface of substrate 530, which isremoved with chemical mechanical polishing (CMP). Then layer 520 isgrown/deposited on substrate 530. The thickness of layer 520, which maybe silicon dioxide, may affect the thickness of the spring layers usedin an accelerometer implementation. For example, layer 520 maycorrespond to spring layer 230 d on substrate 230 in accelerometer 200.Thus, in some embodiments, precise thickness control of layer 520 may beused during deposition.

Turning now to FIG. 5C, a bottom portion of substrate 530 is removed,for example through grinding and CMP. The removal may be up to thebottom of trenches 515. Then, turning now to FIG. 5D, layer 540 isgrown/deposited on substrate 530. The thickness of layer 540, which maybe silicon dioxide, may affect the thickness of a spring layer used inan accelerometer implementation. For example, layer 520 may correspondto spring layer 230 e on substrate 230 in accelerometer 200. Thus, insome embodiments, precise thickness control of layer 540 may be usedduring deposition. Layers 520 and 540 may be surface patterned for useas spring layers in an accelerometer embodiment.

Turning now to FIG. 5E, using either or both of photo resist and silicondioxide as a mask layer, bulk silicon regions between trenches 515 areetched through substrate 530. In some embodiments, this etching processmay be performed using dry vertical etching techniques, known to oneskilled in the art. In some embodiments, the etching may be omitted; itmay be advantageous to conduct the etching, however, in order todecrease the processing time of the subsequent processing step. Afterthese trenches are etched, bonded wafers are placed into XeF₂ (gaseous)for isotropic release of substrate 530. Silicon dioxide covering allsurfaces (i.e., through layers 520 and 540 and filled trenches 515) ofsubstrate 530 act as a masking layer. Substrate 530 is etched as shownin FIG. 5E, leaving cavities 550. As discussed above, vacuum-sealing, orvacuum-packaging, cavities 550, implemented in an accelerometer, mayavoid some of the disadvantages of Brownian noise.

Turning now to FIG. 6, a method in accordance with one embodiment ofthis disclosure is provided. Flow begins at step 600.

At step 600, a survey vessel tows a streamer including at least oneaccelerometer in accordance with this disclosure. In variousembodiments, the streamer may include a plurality of accelerometers inaccordance with this disclosure, and it may also include other sensors(e.g., pressure sensors and/or electromagnetic sensors). In someinstances, the survey vessel may tow a plurality of such streamers. Flowproceeds to step 602.

At step 602, one or more seismic sources are actuated. These may belocated on the survey vessel, towed by the survey vessel, towed by adifferent vessel, etc. Seismic energy from the seismic sources travelsthrough the water and into the seafloor. The seismic energy thenreflects off of the various geophysical formations. Various portions ofthe seismic energy may then be reflected upward toward the streamer, insome instances incorporating time delays and/or phase shifts that may beindicative of the geophysical formations. Flow proceeds to step 604.

At step 604, seismic energy is received at the accelerometers located onthe streamers. Different portions of the seismic energy may reach theaccelerometers either directly from the seismic sources, or after one ormore reflections at the seafloor and/or water surface. Data based on thereceived seismic energy may then be used to infer information aboutgeological structures that may exist under the seafloor. Flow ends atstep 604.

Turning now to FIG. 7, an additional method in accordance with oneembodiment of this disclosure is provided. Flow begins at step 700.

At step 700, a survey vessel tows streamers including acoustictransmitters, and also including accelerometers in accordance with thisdisclosure. In some instances, the acoustic transmitters and theaccelerometers may be combined into an acoustic transceiver. Flowproceeds to step 702.

At step 702, one or more of the acoustic transmitters are actuated. Theacoustic energy produced by the transmitters may travel through thewater toward the other streamers. Flow proceeds to step 704.

At step 704, the acoustic energy is received by an accelerometer. Thedelay between the actuation of the acoustic transmitters and thereception at the accelerometer may be based in part on the distancebetween them. Flow proceeds to step 706.

At step 706, the positions of the streamers (or portions thereof) aredetermined. For example, such positions may be determined based on thedistances between pairs of acoustic transmitters and accelerometers.Flow ends at step 706.

One of ordinary skill in the art with the benefit of this disclosurewill understand that various aspects of this disclosure may in someembodiments be implemented via computer systems. Such computer systemsmay in some embodiments include various types of non-transitorycomputer-readable media, such as hard disks, CDs, DVDs, RAM, ROM, tapedrives, floppy drives, etc.

Although specific embodiments have been described above, theseembodiments are not intended to limit the scope of the presentdisclosure, even where only a single embodiment is described withrespect to a particular feature. Examples of features provided in thedisclosure are intended to be illustrative rather than restrictiveunless stated otherwise. The above description is intended to cover suchalternatives, modifications, and equivalents as would be apparent to aperson skilled in the art having the benefit of this disclosure.

The scope of the present disclosure includes any feature or combinationof features disclosed herein (either explicitly or implicitly), or anygeneralization thereof, whether or not it mitigates any or all of theproblems addressed herein. Accordingly, new claims may be formulatedduring prosecution of this application (or an application claimingpriority thereto) to any such combination of features. In particular,with reference to the appended claims, features from dependent claimsmay be combined with those of the independent claims and features fromrespective independent claims may be combined in any appropriate mannerand not merely in the specific combinations enumerated in the appendedclaims.

Numerous variations and modifications will become apparent to thoseskilled in the art once the above disclosure is fully appreciated. It isintended that the following claims be interpreted to embrace all suchvariations and modifications.

What is claimed is:
 1. A method, comprising: detecting, by at least onesense capacitor within an apparatus, an acceleration of a proof masswithin the apparatus; applying a feedback force to the proof mass via atleast one feedback capacitor, wherein the feedback force is based on theacceleration of the proof mass; and determining an acceleration of theapparatus based on the feedback force.
 2. The method of claim 1, whereinthe detecting the acceleration includes detecting a change incapacitance of the at least one sense capacitor.
 3. The method of claim2, wherein the detecting a change in the capacitance includes: detectinga change in the capacitance of a fully differential set of at least foursense capacitors.
 4. The method of claim 1, wherein determining theacceleration includes determining the Z-axis acceleration.
 5. The methodof claim 1, wherein determining the acceleration includes usingfront-end readout circuitry connected to the at least one feedbackcapacitor.
 6. An apparatus, comprising: a MEMS accelerometer configuredto measure Z-axis acceleration, wherein the MEMS accelerometer includes:a sense electrode configured to detect changes in position of a proofmass in the MEMS accelerometer; and a force feedback electrodeconfigured to provide a restoring force to the proof mass, wherein therestoring force is based on the detected changes in the position of theproof mass.
 7. The apparatus of claim 6, wherein the proof mass isadjacent to at least two vacuum-sealed cavities.
 8. The apparatus ofclaim 6, further comprising a plurality of piezoelectric elementsconfigured to dampen vibrations of the proof mass.
 9. The apparatus ofclaim 6, wherein the MEMS accelerometer includes two sense electrodesarranged in a differential orientation.
 10. The apparatus of claim 6,wherein the MEMS accelerometer includes four sense electrodes arrangedin a fully differential orientation.
 11. The apparatus of claim 6,further comprising closed-loop circuitry configured to measure thedetected changes in the position of the proof mass and configured toapply a voltage to the force feedback electrode.
 12. The apparatus ofclaim 11, wherein the apparatus is further configured to output anacceleration value based on the voltage applied to the force feedbackelectrode.
 13. The apparatus of claim 12, wherein the acceleration valueoutput by the apparatus is the voltage applied to the force feedbackelectrode.
 14. The apparatus of claim 6, wherein the force feedbackelectrode forms a capacitor with an electrode on the proof mass.
 15. Anapparatus, comprising: a central substrate region; a first bondedsubstrate opposing a first surface of the central substrate region; asecond bonded substrate opposing a second surface of the centralsubstrate region; a first sense capacitor and a first force feedbackcapacitor formed between the first bonded substrate and the centralsubstrate region; and a second sense capacitor and a second forcefeedback capacitor formed between the second bonded substrate and thecentral substrate region.
 16. The apparatus of claim 15, wherein thecentral substrate region further includes: a proof mass region boundedby a first spring structure, a second spring structure, a firstprotection structure, and a second protection structure.
 17. Theapparatus of claim 16, further comprising: a vacuum-sealed cavitybounded in part by the first and second bonded substrates, the first andsecond protection structures, a third protection structure, and a fourthprotection structure.
 18. The apparatus of claim 17, wherein the firstand second vacuum-sealed cavities are disposed laterally on either sideof the proof mass region, and wherein the first and second bondedsubstrates are disposed vertically on either side of the centralsubstrate region.
 19. The apparatus of claim 17, wherein the first,second, third, and fourth protection structures include silicon dioxide.20. The apparatus of claim 16, further comprising feedback circuitryconfigured to apply a continuous restoring force to the proof massregion based on measured values of the first and second sensecapacitors.